On the VC-dimension of uniform hypergraphs
نویسندگان
چکیده
Let F be a k-uniform hypergraph on [n] where k − 1 is a power of some prime p and n ≥ n0(k). Our main result says that if |F | > ( n k−1 ) − logp n + k!kk , then there exists E0 ∈ F such that {E ∩ E0 : E ∈ F} contains all subsets of E0. This improves a longstanding bound of ( n k−1 ) due to Frankl and Pach [7].
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